CAT (QA) PYQs

How many $4$-digit numbers, each greater than $1000$ and each having all four digits distinct, are there with $7$ coming before 3?

A four-digit number is formed by using only the digits $1$, $2$ and $3$ such that both $2$ and $3$ appear at least once. The number of all such four-digit numbers is

The number of ways of distributing $15$ identical balloons, $6$ identical pencils and $3$ identical erasers among $3$ children, such that each child gets at least four balloons and one pencil, is